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Pre-Calculus

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How do you solve this quadratic function?
f(x) = −x2 + 10x

  • Pre-Calculus -

    All you have done is define f(x).

    There is no "solution"

    If you had written
    f(x) = (any constant),
    there would be a solution.

  • Pre-Calculus -

    Now, if you want to solve f(x) = 0,

    f(x) = -2x(x-5)

    so, f=0 when either factor is zero. This is why we always set f(x) = 0 to solve for x, because the only time a product of numbers is zero is when one of them is zero. If we had -2x(x-5) = 12, well, that doesn't help us because there are lots of numbers that multiply to equal 12. But if the product is zero, then one of the factors must be zero.

    so, x=0 or x=5 will make f(x) = 0

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